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	BMV tests recent theories that stocks with low idiosyncratic skewness should have high expected returns. For example, Mitton and Vorkink (2007) develop a model that some investors ("lotto investors") have a preference for positive skewness while others ("traditional investors") are mean-variance optimizers seeking to maximize the Sharpe ratio of their portfolios. Lotto investors accept lower average returns on stocks with high idiosyncratic skewness because they have a preference for stocks with lottery-like return properties. In equilibrium, markets clear at prices such that stocks with high idiosyncratic skewness have low expected returns, due to the different portfolio preferences of the two groups of investors.
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	Despite the theoretical basis for the pricing effects of skewness preference, empirically testing the relation is not straightforward as expected skewness is difficult to measure. BMV accounts for the phenomenon that lagged skewness alone does not adequately forecast skewness by presenting a cross-sectional model of expected skewness using additional predictive variables. Using their model, they reaffirm the existing theory that expected idiosyncratic skewness and returns are negatively correlated. Notably, they find the Fama-French alpha of a low-expected-skewness quintile exceeds the alpha of a high-expected-skewness quintile by 1.00% per month. Furthermore, the Fama-MacBeth cross-sectional regressions have statistically significant, negative coefficients. Besides, BMV ﬁnds that the expected skewness helps explain how stocks with low idiosyncratic volatility have high expected returns.
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